Can I use array modifiers to create staggered rows of blocks in a dome?
There is an addon called Building Objects available in blenders addon contrib collection that may come close to what you want. With it enabled you get Add->Mesh->Building Objects->Wall factory to create a wall made of bricks.

While the radial and curve options will give you an igloo like brickwork it doesn't offer any adjustment for the curvature, so this may be a starting point.



If you don't want to install git to get the addons, you can get a snapshot of the contrib repo from here.